Fundamental frequency of a wire wheel spoke

In summary, the fundamental frequency of a wire wheel spoke under tension is 877 Hz, calculated using the equations λn.fn=v and v=sqrt(T/μ), where μ=7860*π*(3.5*10^-3)^2=0.302 kg/m and n=1.
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Any Help
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Homework Statement


The spoke of a wire wheel is 9.5 cm long, 3.5 mm in diameter, and under tension of 2100 N. The wire is made of steel of density 7860 kg/m3. When struck with a metal tool at its center, the spoke rings at its fundamental frequency. What is that frequency?

Homework Equations


λn.fn=v and velocity:v=sqrt(T/μ) , lemda λn=2L/n and L= length of string
fn=n/2L . sqrt(T/μ)
fundamental≡ the first mode ⇒ n=1
μ is the linear mass and must be in kg/m so we must multiply our density by the area which is π.r^2

The Attempt at a Solution


μ=7860*π*(3.5*10^-3)^2=0.302 kg/m
f=1/(2*9.5*10^-2) . sqrt(2100/0.302)
f= 438.8 Hz
but the answer is incorrect why??
 
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I've changed your thread title to more accurately describe the particular problem. Please choose thread titles that are not too general.

Any Help said:
μ=7860*π*(3.5*10^-3)^2=0.302 kg/m
Were you given the radius of the spoke?
 
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  • #3
gneill said:
Were you given the radius of the spoke?
Ah okay. Thanks very much. I used the diameter as a radius wrongly. :)
Now it will be 877Hz which is the correct answer
 

FAQ: Fundamental frequency of a wire wheel spoke

1. What is the fundamental frequency of a wire wheel spoke?

The fundamental frequency of a wire wheel spoke is the lowest frequency at which the spoke will vibrate when plucked or struck. It is determined by the physical properties of the spoke, such as its length, thickness, and material.

2. How is the fundamental frequency of a wire wheel spoke calculated?

The fundamental frequency of a wire wheel spoke can be calculated using the formula f = (1/2L) * √(T/μ), where L is the length of the spoke, T is the tension in the spoke, and μ is the mass per unit length.

3. What factors can affect the fundamental frequency of a wire wheel spoke?

The fundamental frequency of a wire wheel spoke can be affected by several factors, including its length, thickness, material, tension, and the presence of any additional objects attached to the spoke.

4. How does the fundamental frequency of a wire wheel spoke relate to its pitch?

The fundamental frequency of a wire wheel spoke is directly related to its pitch. The higher the frequency, the higher the pitch will be. Therefore, a spoke with a higher fundamental frequency will produce a higher-pitched sound compared to a spoke with a lower fundamental frequency.

5. Can the fundamental frequency of a wire wheel spoke be changed?

Yes, the fundamental frequency of a wire wheel spoke can be changed by altering its physical properties, such as its length or tension. Additionally, attaching objects to the spoke can also change its fundamental frequency. For example, adding a weight to the spoke will decrease its frequency, resulting in a lower-pitched sound.

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